You and a friend have been captured on a desert island ruled by a crazed mathematical despot. You will be locked in separate cells in the island’s prison, and then set the following task:

Every minute for an hour you will each flip a coin. The flips are simultaneous, and after each flip you will make a prediction as to whether the other person’s flip was heads or tails.

So, you both make 60 flips and 60 predictions.

The despot rules that he will kill the two of you if on any one of the 60 predictions you are both correct. (In other words, you both flip, both predict the result of the other person’s flip, and are both right). To escape with your lives at least one of you must predict wrongly each time.

You are given ten minutes to think up a survival strategy before being taken to the cells. Once you are in the cells you cannot communicate with each other, although you are obviously able to see the results of your own flips.

Can you guarantee your survival, and if so, how?

Solution

This puzzle seems difficult at first, requiring some kind of trick or extra clever strategy, but the solution is simple.

You will survive if you use the outcome of your coin flip as your prediction, and your friend uses the opposite of their coin flip as their prediction. (Or vice versa).

So, if you flip heads, you predict heads. If your friend flips heads, they predict tails.